Problem: Solve for $x$ and $y$ using elimination. ${-6x+5y = 15}$ ${5x-4y = -11}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $4$ and the bottom equation by $5$ ${-24x+20y = 60}$ $25x-20y = -55$ Add the top and bottom equations together. ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-6x+5y = 15}\thinspace$ to find $y$ ${-6}{(5)}{ + 5y = 15}$ $-30+5y = 15$ $-30{+30} + 5y = 15{+30}$ $5y = 45$ $\dfrac{5y}{{5}} = \dfrac{45}{{5}}$ ${y = 9}$ You can also plug ${x = 5}$ into $\thinspace {5x-4y = -11}\thinspace$ and get the same answer for $y$ : ${5}{(5)}{ - 4y = -11}$ ${y = 9}$